Teams can't formally contact free agents until 12:01 a.m. ET July 1, but sources told ESPN.com that the Atlanta Hawks and Miami Heat are two more teams that could join the race for Anthony, depending on how things play out before, during and after Thursday's NBA draft.

The Bulls are widely regarded as the early favorite to steal Anthony from the Knicks, with sources saying Monday that Chicago has been quietly planning for this free-agent pursuit for months, going back to the January trade of Luol Deng to Cleveland. Sources say every move Chicago made during the season's second half -- including the seemingly minor signings of veterans Ronnie Brewer, Lou Amundson and Mike James to very tradeable contracts -- was made with the hope they might be helpful in a potential sign-and-trade with the Knicks for Anthony.

Sources say the Rockets, meanwhile, have begun working on trade exits for center Omer Asik and point guard Jeremy Lin to clear enough space under the salary cap to make a representative offer to Anthony. The Rockets have been confident for some time, sources say, that they can not only move both players if necessary in deals that create the requisite flexibility but also rival the Bulls' sales pitch.

The Lakers are in the advantageous position of having enough room under the salary cap to make a maximum offer to Anthony without having to clear any salary, but it is believed Anthony would want them to strengthen their roster before he would seriously consider a move to L.A. Sources say the Lakers, to that end, have been exploring their options with the No. 7 pick in Thursday's draft and have told teams they are prepared to package the pick with the expiring contract of Steve Nash (owed $9.7 million next season) for the right offer.

ESPNDallas.com reported Sunday that the Mavericks, armed with plenty of cap space themselves, likewise expect to be granted a face-to-face sit-down with Anthony. Yet Mavs star Dirk Nowitzki, who also is bound for free agency July 1, has acknowledged that the Bulls and Rockets have better odds of prying Anthony out of New York, labeling Dallas' chances "not really" realistic.

Earlier this month, ESPN.com reported the Heat had begun internal discussions about pursuing the former scoring champion to try to grow their Big Three into a Big Four, but the Heat could pursue Anthony only if LeBron James, Chris Bosh and Dwyane Wade opt out of their current deals later this week and are willing to take less money to re-sign and play alongside Anthony. Heat president Pat Riley has since confirmed the club has pondered pursuing Anthony but conceded the scenario is a "pipe dream" given the financial complexities involved.

The Hawks would have to clear approximately $10 million to $12 million in salary-cap space to pursue Anthony, but sources indicate that is one of the many options Atlanta is considering, making it a sleeper team to watch.

Anthony is eligible to sign a maximum contract worth $129 million over the next five seasons with the Knicks. A max deal with a new team is $96 million over four years.

"Carmelo loves being a Knick, he loves the city and he loves the fans," Leon Rose, Anthony's agent, said Monday. "At this stage of his career, he just wants to explore his options."

In an online interview that aired Monday, Anthony said uprooting his family to another city could not be dismissed as a factor amid the rising speculation about the Bulls' desire to team him with Derrick Rose, Joakim Noah and hard-driving coach Tom Thibodeau.

In the interview with Vice Sports taped June 3, Anthony said: "The average person just sees the opportunity to say that, 'Oh, Melo should go here, Melo should go there. I think he should do this, I think he should do that.' But they don't take into consideration the family aspect of it. Your livelihood. Where you're going to be living at. Do you want your kids to grow up in that place? In that city? Do I want to spend the rest of my career in that situation in that city? So all of that stuff comes into play.

"My son goes to school [in New York]. He loves it here. To take him out and take him somewhere else, he has to learn that system all over again, he has to get new friends. And I know how hard it was for me when I moved from New York to Baltimore at a young age. Having to work your way to try to make friends.

"As far as this goes, basketball goes, it's hard to just say, 'OK, I'm going to go here, I'm going to make this decision, I'm going to do that.' Because everybody's affected by that."

New Knicks president Phil Jackson tried for weeks to convince Anthony to opt in for the final season on his current contract and delay his free agency until the summer of 2015. But Anthony maintained all season that he intended to become a free agent this summer and, according to a report last week from ESPN New York's Ian Begley, already has begun researching the city of Chicago.

Thibodeau, meanwhile, has reached out to some of Anthony's former coaches to inquire about the seven-time All-Star, according to a recent report in the Chicago Sun-Times. And ESPN.com reported in March that Anthony and Noah talked about playing under Thibodeau during the All-Star break in a conversation that turned into a recruiting pitch from Noah to Anthony.

Jackson said late last month that he's "not losing sleep" over Anthony's free agency but is "definitely concerned" about the idea of Anthony signing elsewhere. Anthony has said publicly that he would like to stay in New York but also wants to be in position to win an NBA championship.

The Knicks are coming off a 37-45 season under the fired Mike Woodson and don't have salary-cap space to seriously retool the roster around Anthony until the summer of 2015.

Information from ESPNNewYork.com's Ian Begley and ESPN.com's Brian Windhorst was used in this report.